one or more of the aforementioned conditions are not satisfied by the differential equation, it should be first reduced to the polynomial form in which it satisfies all of the above conditions. If a differential equation is not expressible to polynomial equation form having the highest order derivative as the leading term then that the degree of the differential equation is not defined. The determination of the degree of a given differential equation can be tricky if you are not well versed with the conditions under which the degree of the differential equation is defined. So go through the given solved examples carefully and master the technique of calculating the degree of the given differential equation just by sheer inspection!
Examples for the calculation of degree: ( ) Consider the differential equation d y − = sin Ordinary Differential Equations The highest order derivative involved here is , and its power is in the equation. Thus, the order of the differential equation is and degree is . ( ) Consider the differential equation + = y d y dx . Since this equation involves fractional powers, we must first get rid of them.
On squaring the equation, we get + = d y Now, we can clearly make out that the highest order derivative is . Therefore order of the differential equation is and since its power is in the equation, the degree of the differential equation is . ( ) Consider the differential equation sin dy d y + . Here, the highest order derivative is .
Because of sine of first derivative, the given differential equation can not be expressed as polynominal equation. So, the order of the differential equation is , and, it is not in polynomial equation in derivatives and so degree is not defined. ( ) Consider the equation e x dy d y sin( ) Here, the highest order derivative (order is ) has involvement in an exponential function. This